(ingles)calculo diferencial

7/29/2019 (Ingles)Calculo Diferencial

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CALCULO DIFERENCIAL

TECHNICAL UNIVERSIDADMANAB

FACULTY OF COMPUTER

Engineering in Information Systems

Differential calculus POTAFOLIO

SECOND HALF OF RACE

2ND. "A"

STUDENT NAME

JUAN PABLO DUEAS VILLACIS

TEACHING

ING. Jos Cevallos S.

POROTVIEJO November, 2012

SEMESTER

SEPRIEMBRE 2012 February 2013


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__________________________________________________________________

Mission of the School of Computer Science

Being a unit with high academic prestige, efficiency, transparency and quality ineducation, organized in their activities, protagonist of regional and nationalprogress.

Vision of the Faculty of Computer Science

How effective professionals in the field of Computer Science, with honesty, fairnessand solidarity, provide answers to the needs of society by raising their standard ofliving.

Mission of the Technical University of Manabi

Being academics, scientists and professionals responsible, humanistic, ethical andcaring, committed to the goals of national development, which contribute to solvingthe country's problems as university teaching with research, able to generate andapply new knowledge, encouraging the promotion and dissemination of knowledgeand culture, under the Constitution of the Republic of Ecuador.

Vision of the Technical University of Manabi

Being university, leader and reference of higher education in Ecuador, promotingthe creation, development, transmission and dissemination of science, technologyand culture, social recognition and regional and global projection.

__________________________________________________________________

CURRICULUM VITAE

NAMES: John Paul

SURNAMES: Villacis Dueas

DATE AND PLACE OF BIRTH: Quito, June 15, 1993

IDENTITY CARD: 171903910-7


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MARITAL STATUS: Single

ADDRESS: PORTOVIEJO

Real Av Portmore JointTamarindos Real. House 5.

TELEPHONES: 05-2-442413 Cel: 084257083

STUDIES:

PRIMARY: Charles Darwin Education Unit (Quito)

SECONDARY: Santo Tomas Education Unit (Portmore)

SUPERIOR:-Technical University of Manabi: Currently in 2nd semester of SystemsEngineering

COURSES:Computer Course Windows 95, Word, Excel. Computer Course"Computer Center".

WORK EXPERIENCE:

- P.FPreparador Physical, Technical Assistant Academy AT Alfaro Moreno (Manta-Portoviejo)

PERSONAL REFERENCES:

Dr. Jorge Villacis Tel: 052639002

__________________________________________________________________


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Technical University of ManabiFACULTY OF COMPUTEREngineering inInformation SystemsSELF

My name is John Paul VILLACIS DUEAS am a student of the subject ofdifferential calculus, currently the second semester course at the Faculty ofComputer Science at the Technical University of Manabi. I am a responsible,organized and I like working in teams.

My goals are to become a professional engineer systems are: Get the attitudesand skills necessary for employment in any field desempearnos,desenvolvindome easily and with the ability to solve any problem that comes ourway. Achieving success, joining such a team delivering all my knowledge and

learn total available daily in order to overcome projects agreed and so thereforehave an economic availability to continue with my studies and achieve personalgrowth expectations . Use my knowledge of systems engineer at work that keepdeveloping my invite, a job that allows me to increase my abilities and whichmakes me grow personally and professionally.

__________________________________________________________________


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Technical University of ManabiFACULTY OF COMPUTEREngineering inInformation SystemsDAILY METACOGNITIVE

Class No. 1:Period: from 24 September 2012 to 24 Febr 2013TIME: 4 HOURS INTWO DAYS 2 HOURSDATE: Tuesday, September 25-Thursday, September 27,

2012.TEACHER GUIDE: Jos Cevallos Salazar1. ENTRY STUDENTS2. Coursepresentation3. VIDEO OF REFLECTION: Bamboo4. GENERAL VIEWINGCOURSE calculus5. CHOICE OF TEACHING ASSISTANT FACILITATOR6.TEACHING PORTFOLIO PRESENTATION previous semester.7. INTRODUCINGTHE CURRENT SEMESTER POTAFOLIO CONCERNING THECONTENTS:1.CURRICULUM OF TEACHING2. TEACHING PHILOSOPHY3. ITEM TOQUALIFY: WORK, written tests, PROJECTS,WORKSHOPS AND PORTFOLIO.8.EXPLANATION OF MODEL STUDENT PORTFOLIO ASEVIDENCE ANDCONTINUOUS IMPROVEMENT.9. DELIVERY OF MATERIAL TOTAL LOGICALCALCULUS COURSEDIFFERENTIAL.10. HOW TO QUALIFY11. COURSE

POLICIES12. Class content:1. FUNCTION:2. METHOD: deductive, inductive andreflective3. TECHNICAL brainstorming.4. WORDS OF THE CLASS:1.FUNCTION2. RELATIONSHIP3. GRAFO4. DOMAIN5. Codomain6. Input set7.IMAGE (I) TRAVEL (Rc), RANGE (Rg)8. SET OF ARRIVAL9. VARIABLES:independent, dependent10. CONSTANT11. Cartesian product12. PAR5.FUNCTION INPLICITA13. Explicit function14. Increasing function15. DecreasingfunctionTOPIC DISCUSSED: UNIT I:6. - Graphing7. - IDENTIFICATION OFFUNCTIONS: numerical method and graph-CRITERION verticalline.PrefaceFunction analysisCartesian productDefinition: GraphingRelations:

Definition, domain and range of a relation.Functions: Definition, notationDomain,path or range of a functionVariables: dependent andindependentConstantGraphing a functionCriteria vertical line.PerformanceObjectives:Define and recognize: Cartesian product, relations and functionsDefineand recognize: domain and image of a functionDefine and plot functions,identifying the same criteria apply.General competence: Definitions, identificationand graphic strokes.INTRODUCTIONThe following summary information isdisclosed on the # 1 class in differential calculus which began with a briefexplanation of the respective chapter. In the first class we took into account severalfactors on the functions as:Domain. 2. Co-domain. 3. Image.ABSTRACTIt began

with the presentation of the teacher, how to work with him, he showed us a videoentitled "A lunch with God", one at each table representative gave his thoughts onthe presentation about the video, was elected assistant and we introduced theportfolio of the previous semester teaching and teacher's current portfolio also sawa student portfolio. In the first class of "Episode # 1" is the explanation given for theissue related to "Features" section above for the taking as the beginning of classthe following topic: "Relations, Functions - Variables, Cartesian product" The


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to be composed of a domain and a condominiumCartesian plane, being formed bytwo lines, one horizontal and one vertical cut into a point.

We also saw how to recognize a function by the criterion of vertical line in aCartesian plane, this is done by passing a perpendicular line parallel to the

ordinate (y) by cutting a feature point is, if two or more short not function.Cartesianproduct. The Cartesian product allows us to graphically represent any function, if itis explicitly and corresponding check is carried out by applying the "Criterion of theline".

Function No Function

The criterion of the line. The criterion of the line indicates, by drawing a vertical lineis formed parallel to the ordinate because cutting a point on the graph and connectyour domain to one and only one time with your image B.We practice where wecan see if there are functions in relationsy = 2x +1This is a function for that andhave a result.y2 = 4-x2If we solve this exercise will look like this:y2 = 2-x2y = (4-2x)This is not a function and have it as two different signed result.Other detailswe discussed were:Resultf (x)

SortGalare, is the data summary table example:x y

-4 25 -3 16 -2 9 -1 4 0 1What things were difficult?, What were easy, What Ilearned today?

The differential calculus class left me much teaching as I understand better"Relations, Functions - Variables, Cartesian product". And the participation of myclassmates for the explanation of each Cartesian product on the board, mysuggestion is to stay the same method to remain active study that is important forthe student to come to understand the best matter manner.


Class No. 2:Period: from 24 September 2012 to 24 Febr 2013TIME: 4 HOURS INTWO DAYS 2 HOURSDATE: Tuesday, October 2, Thursday, October 4,2012.TEACHER GUIDE: Jos Cevallos Salazar1. ENTRY STUDENTS2. VIDEOOF REFLECTION: SEARCH3. TECHNICAL: Brainstorming4. CONTENTS OF THECLASS:1. FEATURES:2. GRAPHIC FUNCTION IN THE SOFTWARE MATLAB3.


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FIND FUNCTION AND IMAGE DOMAIN4. Objective situations where it involvesthe concept of function, Silva Laso, 8675. Function in the Royals: function injective,surjective and bijective, Silva laso, 142, 8746. Charts, horizontal line criterion, SilvaLaso, 8767. Types of functions:8. Constant function, Silva Laso, 891, Smith, 149.Power function: identity function, quadratic, cubic, hyperbole, and equilateralroot

function, Silva Laso, 919, Larson, 375. figure (1);6. >> Syms x;7. >> Y = ((x ^ 2) / (x+1));8. Ezplot >> (y);TOPIC DISCUSSED: UNIT I:Features:Objective situationswhere it involves the concept of functionFunction in the Royals: function injective,surjective and bijectiveGraphic, horizontal line criterionTypes of functions:ConstantFunctionPower function: identity function, quadratic, cubic, hyperbole and rootfunctionPerformance Objectives:Define mathematical models which involves theconcept of functionDefine, recognize and graph various types of functions.General

jurisdiction:Define mathematical models, draw graphs of different types offunctions.Facts discussed today:We start with the video of reflection with the name

"Brainstorm", this is treated as that briefly had one dawned with their joys andconcerns. Open the program MATLAB, to verify the operation of such a program,doing some exercises like: >> figure (4)

y = (x-1) / (x)

y = (x-1) / x>> Ezplot (4)What things were difficult?, What were easy, What Ilearned today:This class left me much teaching as I could better understand mysuggestion is to stay the same method to study whether virtual or not remainsactive but that is important for the student to come to understand the best way thematter. Most of the item is not trying hard hiso me before it was the opposite

because the teacher's explanation easy hiso I learn a little about this subject and Ilearned today in the actual functions to find domain and image expressing them insets. I would like to maintain the teaching technique of Engineer Jos Cevallos.


Class No 3:Period: from 24 September 2012 to 24 Febr 2013TIME: 4HOURSDATE: Tuesday, August, Thursday, Sept. 10. of 2012.TEACHER GUIDE:Jos Cevallos Salazar

ENTRY STUDENTS2. VIDEO OF REFLECTION: QUALITY HUMAN3.TECHNICAL: Brainstorming4. CONTENTS OF THE CLASS:Types of functions:polynomial function, Silva Laso, 920, Larson, 37 rational function, Silva Laso,


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949, Smith, 23 Functions sectioned, Silva Laso, 953 algebraic function.Trigonometric functions. Silva Laso, 598, 964, Smith, 33 exponential function,Silva Laso, 618, Smith, 41 Inverse, Silva Laso, 1015 logarithmic function:definition and properties, Silva laso, 618 inverse trigonometric functions, J.Lara, 207, Smith, 454 Transformation functions: quick technical graphing

functions, Silva Laso, 973,Topic discussed: Unit I:Types of functions:Polynomialfunction.Rational function.Functions sectioned.Algebraic function.Trigonometricfunctions.Exponential function.Inverse function.Logarithmic function: definition andproperties.Inverse trigonometric functions.Transformation of functions: quickgraphing technique functions.

PERFORMANCE OBJECTIVES:Define, recognize and graph various types offunctions.

GENERAL DUTIES:Plot graphs of different types of functions

SUMMARY OF THE CLASSHe started the class with the theme of reflection"LETTER OF 2070" that it was a letter written by an inhabitant of the earth in theyear 2070, in which he describes the deplorable living situations, such as lack ofwater shortly oxygen and other things that make us think and reflect that if we donot take care of our planet is not going to last long.

What things were difficult?The issues are more difficult to understand how to solvea polynomial function, graphing hyperbolas that are part of the cone and thegraphs of the functions sectioned.What was easy?What is easier to learn to mewas sectioned and graphics functions absolute value functions through the galleyand graficarlas in the Cartesian plane.What did I learn today?Today I learnedthanks to reflective video still time to save the paneta also learned to graphalgebraic functions as part of the hyperbolas, rational functions, linear functions,sectioned functions, absolute values by the method of the galleys.

Technical University of ManabiFACULTY OF COMPUTEREngineering in

Information SystemsDAILY METACOGNITIVEClass No 4:Period: From September24, 2012 to February 23, 2013TIME: 2 HOURSDATE: Tuesday, 16 of2012.TEACHER GUIDE: Jos Cevallos Salazar

1. ENTRY STUDENTS2. VIDEO OF REFLECTION: Trust me3. TECHNICAL:Brainstorming4. CONTENTS OF THE CLASS:Combination of features: Algebraof functions: Definition of addition, subtraction, product and quotient of


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functions,Silva Laso, 994 Composition of functions: definition of compositefunction, Silva Laso, 999APPROACH TO THE IDEA OF LIMIT.Limit of a function

Limit Concept: Properties of limits, Silva Laso, 1029, 1069, Smith, 68, Larson,46indeterminate boundaries, Silva Laso, 1090Sided limits Limit Right, Silva

Laso, 1041 Left Limit Limit bilateralPERFORMANCE OBJECTIVES:

Define Operations with Functions. Define and calculate limits.Topic discussed:Unit I:Combination of features:Algebra of functions: Definition of addition,subtraction, product and quotient of functions.Composition of functions: definitionof composite function.Limit of a functionLimit Concept: Properties oflimits.Indeterminate boundaries.Sided limitsRight-hand limit.Left limit.Bilaterallimit.PERFORMANCE OBJECTIVES:Define operations functions.Define andcalculate limits.GENERAL DUTIES:Defining operations and functions limitcalculation using criteriaSUMMARY OF THE CLASSThe class begins withthoughtful video "Here I am", which tells us that we will have someone always be

there to help, advise and support us.What things were difficult?Things that made me the issue was complicatedtrigonometric functions with their inverse trigonometric functions.What waseasy?For me it was easier to plot the absolute value function and functionsectionedWhat did I learn today?I learned about trigonometric functions, inversetrigonometric functions, exponential function with its properties, logarithmicfunctions, and also the greatest integer functions, functions and inverse functionssign, but to be honest I'm not entirely clear but that's what the supports thatfacilitated the teacher.

Technical University of ManabiFACULTY OF COMPUTEREngineering in

Information SystemsDAILY METACOGNITIVEClass No 5:Period: From

September 24, 2012 to February 23, 2013TIME: 4 HOURS IN TWO DAYS 2

HOURSDATE: Tuesday, 23-Thursday, October 25, 2012.TEACHER GUIDE:

Jos Cevallos Salazar

1. ENTRY STUDENTS2. VIDEO OF REFLECTION: REMEMBER WHEN SAD3. TECHNICAL:

BrainstormingCONTENTS OF THE CLASS:Infinite limit: Definition, theorems, Silva Laso, 1090,Larson, 48DEADLINE TO INFINITY: Definition, theorems. Limit infinity and infinity, Smith,

95ASYMPTOTES: vertical asymptotes, definition, graphics, Silva Laso, 1102, Smith, 97

Horizontal Asymptotes, definition graphics. Asymptotes oblique definition

graphics.PERFORMANCE OBJECTIVE Define and calculate infinite limit, to infinity and infinity

and infinity. Define and graph asymptotes horizontal, vertical and oblique.GENERAL DUTIES:

definition and calculation using criteria limits, asymptotes tracing application.Topic discussed: Unit


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I:Infinite limit:Definition, theorems.DEADLINE TO INFINITY:Definition, theorems.Limit infinity and

infinity.ASYMPTOTES:Vertical asymptotes, definition graphics.Asymptotes horizontal definition

graphics.Oblique asymptotes, definition graphics.PERFORMANCE OBJECTIVEDefine and calculate

infinite limit, to infinity and infinity and infinity.Define and graph asymptotes horizontal, vertical

and oblique.GENERAL DUTIES:Definition and calculation using criteria limits, asymptotes tracing

application.SUMMARY OF THE CLASSWe began the class with the video "Nobody will love you likeme." Which leaves us thinking that you can love someone and if you do you must do so in a good

way and with that things will work out and there will be happiness.

What things were difficult?The only thing I saw were complicated theorems of limits on the books

of Silva Lasso.What was easy?

The things I did was easy to solve boundary functions when the limit approaches infinity.What did

I learn today?Today we learned about the limits, when there is continuous or discontinuous

function function well when its discontinuity is renewable.

Technical University of ManabiFACULTY OF COMPUTEREngineering in Information SystemsDAILYMETACOGNITIVE

Class No 6:Period: From September 24, 2012 to February 23, 2013TIME: 2 HOURSDATE: Tuesday,

October 30, 2012.TEACHER GUIDE: Jos Cevallos Salazar

1. ENTRY STUDENTS2. VIDEO OF REFLECTION: giving and receiving3. TECHNICAL:

BrainstormingCONTENTS OF THE CLASS:Trigonometric LIMITS: Trigonometric Limit fundamental

Laso Silva, 1082, Larson, 48 Theorems.CONTINUITY OF A FUNCTION IN A NUMBER:

Definition, Silva Laso, 1109 continuity criteria. essential removable

discontinuity.PERFORMANCE OBJECTIVES: Define and calculate trigonometric limits. Define

and demonstrate the continuity or discontinuity of a function.GENERAL DUTIES: Definition and

calculation of trigonometric limits, continuity and demonstrationapplying criteria discontinuity

function.Topic discussed: Unit I:Trigonometric LIMITS:Basic trigonometric

limit.Theorems.CONTINUITY OF A FUNCTION IN A NUMBER:Definition.Continuity

criteria.Removable discontinuity essential.

PERFORMANCE OBJECTIVES:Define and calculate trigonometric limits.Define and demonstrate the

continuity or discontinuity of a function.GENERAL DUTIES:Definition and calculation of

trigonometric limits, demonstrating continuity and discontinuity of functions using

criteria.SUMMARY OF THE CLASSThe video class started thinking "Do not give up", which pretty

much encouraged by never giving more difficult the obstacle, because if we fulfill our purposes the

rewards will be immense.What things were difficult?It hampered me the graph of the continuous

function on the boundary.What was easy?How easy was some limits exercises practiced with

supporting materials.What did I learn today?I learned that the limit of a trigonometric function is

the value taken by the variable.


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Technical University of ManabiFACULTY OF COMPUTEREngineering in Information SystemsDAILY

METACOGNITIVE

Class No 7:Period: From September 24, 2012 to February 23, 2013TIME: 4 HOURS IN TWO DAYS 2

HOURSDATE: Tuesday, June-Thursday, November 8, 2012.TEACHER GUIDE: Jos Cevallos Salazar

1. ENTRY STUDENTS2. VIDEO OF REFLECTION: THE BASKET3. TECHNICAL:

BrainstormingCONTENTS OF THE CLASS:Calculus.Slope of the line tangent: Definitions,

Silva laso, 1125, Smith, 126 Larson, 106Derivative: definition of the derivative at a

point, Smith, 135 Geometric interpretation of the derivative. The derivative of a

function Graph of the derivative of a function, Smith, 139 Differentiability and

continuity. Larson, 112PERFORMANCE OBJECTIVES: Define and demonstrate the slope

of the tangent line at a point on the curve. Define the derivative of a function.GENERALDUTIES: Application of defining the slope of the tangent line and derivativedifferent

types of functions.Topic discussed: Unit I:Slope of the line

tangent:DefinitionsDerivative:Definition of the derivative at a pointGeometric

interpretation of the derivative.The derivative of a functionGraph of the derivative of a

functionDifferentiability and continuity.PERFORMANCE OBJECTIVES:Define and

demonstrate the slope of the tangent at a point on the curve.Define the derivative of a

function.GENERAL DUTIES:Applying the definition of the slope of the tangent line and

derived in different types of functions.SUMMARY OF THE CLASSThe last class of the first

set began with the issue of derivativesWhat things were difficult?Formulas derived from 8

onwards as they were new to me.What was easy?How easy formulas 1 through 7 becauseI had already seen at school.What did I learn today?To solve the formulas derived from 8

onwards.


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2DO CICLO

Technical University of Manabi

FACULTY OF COMPUTER calculus

SECOND HALF OF RACE

CLASS No 8

Period: from September 24. 2012 to 24 Febr. , 2013

TIME: 4 HOURS IN TWO DAYS 2 HOURS

DATE: Tuesday-Thursday 2012.

TEACHER GUIDE: Jos Cevallos Salazar

CONTENTS:

PROJECT PRESENTATION.

Project type.

Name of contribution.

IT tools.

Description.

Learning Objective.

Project duration.

Requirements.

Resources and materials.

activities and team teaching.

Evaluation Criteria.

PERFORMANCE OBJECTIVES:

Strengthen their knowledge potential.


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Provide experiences.

Troubleshoot critics.

Link the team with the community and the family.

GENERAL DUTIES:

What things were difficult?

I found no difficulty.

What was easy?

It became easy to understand the gaps resulting from the work and mathematical models

What did I learn today?

In this class I learned to develop issues arising such as trigonometric functions.

CLASS # 8

My contribution to the group:

The contribution made by the on my part was to develop issues arising such as

trigonometric functions.

TECHNICAL UNIVERSITY FACULTY OF COMPUTER MANAB calculus

SECOND HALF OF RACE

CLASS No 9



DATE: Tuesday, December 4, Thursday, December 6, 2012.TEACHER GUIDE: Jos Cevallos Salazar

CONTENTS:

Plenary everyday derivative

Lesson on board.


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REFLECTION:

Renew die

Calculation of derivatives of some functions of algebraic type.

Derivative of constant function, Silva laso, 1137, Smith, 145, Larson, 118

Derivative of function identically.

Derivative of the power function.

Derivative of a constant function.

derived from the sum of functions.

Product Derivative of functions.

Derivative of the quotient of two functions.

Derivative of a composite function.

chain rule, Silva Laso, 1155, Smith, 176, Larson, 141

Power Rule combined with the chain rule.


Define and calculate the derivative of some functions of algebraic type.

Define and calculate derivatives of composite functions.

Define and apply the rule of the open string.

GENERAL DUTIES:

Direct and rightly mathematical models of the variation of different types of functions.

CLASS No 9

REFLECTION: RENEWED TO DIE

Each of us lives among unique circumstances. From birth to death to walk through a world

full of vicissitudes. There are those who manage to have wonderful families, others fail in

the attempt, some achieve great fame in their jobs, others simply go unnoticed.


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With the current economic crisis many people have a hard life, with enough effort,

approaches the level of survival. Other people live in opulence material while in spiritual

self-destructs. Each person is unique and unrepeatable and goes through a series of

features and peculiarities that make their life journey. To this we add endless

unrepeatable situations and places that impress everyone and mold it to change its

character. So many factors result in a special person.



I was not anything difficult, since the debate is one of the techniques studies retentive ns

allows themes to help us in our teaching-learning process.

What was easy?

Everything was very simple, I referred in these classes helps us learn more and more.


I learned new things about the derivative.


SECOND HALF OF RACE

CLASS No 10



DATE: Tuesday, December 11th-Thursday, December 12, 2012.


CONTENTS:

Exponential Functions

inverse trigonometric functions

REFLECTION:

The perfect peace.


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POWER derivative function for rational exponents. Laso Silva, 1139,

Smith, 145

DERIVED trigonometric functions. Silva laso, 1149, Smith, 162 Larson, 135

IMPLIED ARISING:

Method of implicit differentiation. Silva Laso, 1163, Smith, 182 Larson, 152

DERIVED exponential and logarithmic functions:

Derivative of exponential functions. Smith, 170, Larson, 360

Derivative of exponential functions of base e.

Derivative of logarithmic functions.

Derived from natural logarithm function.

logarithmic differentiation.


Define and calculate derivatives of functions with rational exponents.

Define and calculate derivatives of exponential and logarithmic functions.

Define and calculate derivatives of implicit function.

GENERAL DUTIES:

Application of mathematical models to derive direct and rightly different types of

functions

Derivation of Exponential Functions

We know that e is an irrational number, then e = 2.718281828 ... The notation e for this

number was given by Leonhard Euler (1727).

The function f (x) = ex is a natural exponential function. As 2


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Scientific calculators contain a key to the function f (x) = ex. Geometrically the slope of the

graph of f (x) = ex at any point (x, ex) is equal to the y coordinate of that point. For

example, in the graph of f (x) = ex point (0.1) the slope is 1.

CLASS No 10

REFLECTION: PERFECT PEACE

He is at peace with ourselves helps us keep things in a calm manner without making

mistakes that one day can change our lives to be bad and likewise peace with others and

strengthen us and grow as people.



I was a bit complicated as these features their formulas are slightly different from eachother and difficult to learn them m.

What was easy?

Your procedure once identified and function.


In this class I learned to develop trigonometric and exponential functions.


SECOND HALF OF RACE

CLASS No 11



DATE: Tuesday, 18th of December, Thursday, Dec. 20, 2012.


CONTENTS:

Open Strings

Implicit Derived


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REFLECTION:

Importance of Strategy

DERIVATIVE FUNCTION

Inverse trigonometric. Smith, 459, Larson, 432

SUPERIOR order derivative.

common notations for higher derivatives. Silva Laso, 1163, Smith, 149

APPLICATION OF THE DERIVATIVE. Silva Laso, 1173

EQUATION of the tangent line and the normal line to the curve at a point. MAXIMUM AND

MINIMUM VALUES. Silva Laso, 1178, Smith, 216, Larson, 176

Absolute maximum and minimum of a function.

local maxima and minima of a function.

Extreme Value Theorem.

Critical points.


Define and calculate higher derivatives

Apply the derivative in equation of the tangent line, maximum and minimum values.

GENERAL DUTIES:

Implementation of the derivative in optimization problems.

Chains open

It is a process that allows us to evaluate a function in terms of another, ie composite

function.

Z = x

Y = LNZ

dz / dy = 1/2 x dy / dx = dz / dx. dy / dz

dy / dx = 1 / z dy / dx = 1/2 x 1 / z


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dy / dx = x 1/2z

dy / dx = 1/2 x x = 1/2x

dy / dx = 1/2x / /

CLASS No 11

REFLECTION: IMPORTANCE OF STRATEGY

The strategy is all for a good gesture ... and competent professionals.

Have trouble is inevitable .. being defeated is optional



I was making it difficult for open strings.

What was easy?

The process of deriving implicit because it is simple, and once all the derivatives studied.


In this class I learned to develop broadcast and Implicit Derived.


SECOND HALF OF RACE

CLASS No 12



DATE: Tuesday, Thursday, Dec. 27, 2012.


CONTENTS:

Implementation of the derivative


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peak and lowest point

REFLECTION:

Rain

Monotonic functions AND 1ST TEST. Derivative:

increasing function and decreasing function: definition. Silva Laso, 1179, Smith, 225,

Larson, 176

monotonic function tests.

First Derivative Test for local extreme.

Concavities and TURNING POINT:

concave up and concave down: definition. Silva Laso, 1184, Smith, 232

Test concavities.

Turning point: definition.

Test the 2nd. Derived for local extremes.

STROKES OF CURVES:

Information required for plotting curves: domain, coordinates the origin, point of

intersection with the axes, symmetry and asymptotes.

Information 1st. and 2nd. Derivative.


Apply the information of the 1st. and 2nd derivative at the stroke of graphs.

GENERAL DUTIES: Implementation of the derivative in optimization problems.

Increasing and decreasing function

A function is increasing on an interval if for any two values of the interval, and is satisfied

that:

It increased when the Y values are increasing or staying with increasing X.

It increased when the Y values are decreasing or staying with increasing X.


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If a function has a constant value of Y, then it is constant, but falls within the definition of

both growing and declining.

If the function only grows or decreases only (has no leg she is stable, not growing or

decreasing), then is said to be strictly increasing or strictly decreasing, as appropriate.

Definition:

If increasing the value of x the value of its image ((x) also increases, it is said that the graph

of the function increases and, conversely, when the value x increases decreases ((x), we

say that the function decreases.

Symbolically we can define:

(Is increasing on an interval [a, b] ((x1 (x2 ([a, b]: x1 (x 2 ((x1) (((x2)

(Is decreasing on an interval [a, b] ((x1 (x2 ([a, b]: x1 (x 2 ((x1) (((x2)

[Pic]

Criteria for increase and decrease

Let f be a continuous real variable function on the closed interval [a, b] and differentiable

on the open interval (a, b).

i. If [pic] for all [pic] then f is increasing on [a, b].

ii. If [pic] for all [pic] then f is decreasing on [a, b].

iii. If [pic] for all [pic] then f is constant on [a, b].

Comment:

The increase and decrease of the curve coincide with the sign of the first derivative. Thus:

where [pic] (positive derivative), f (x) is increasing.

[Pic] (negative derivative), f (x) is decreasing.

The sub Theorem 5.1.2, to classify the relative extrema (maximum and minimum) of afunction, according to changes in sign of the first derivative.

CLASS No 12

REFLECTION: THE RAIN


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That despite the problems i difficulties in our lives, we must learn to take things on and

learn to solve.



I was not at all difficult.

What was easy?

It became easy to find the maximum and minimum.


In this class I learned to find maximum and minimum.


SECOND HALF OF RACE

CLASS No 13



DATE: Thursday, March Tuesday, Thursday, January 3, 2013.


CONTENTS:

Problems finding derived using the maximum.

Integral

Optimization problems.

Problem of highs and lows. Silva Laso, 1191, Smith, 249, Larson, 236PERFORMANCE OBJECTIVES:

Apply the derivative information on maximum and minimum problems.

GENERAL DUTIES:

Definition of optimization problems.


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Integral calculus: definition.

This is what we have studied in the infinitesimal calculus they call "Differential Calculus".

Now we will focus on another part of this, they call "Integral Calculus".

Find a function from its derivative fa, involves the finding of a family of functions whosederivative can be f; these functions are called anti derivative, since it is necessary to find

the reverse to take the bypass and this process is called "integration." In a similar way we

can conclude that the problem with this is, if we have the speed of a moving point, we can

find its path or if we have the slope of a curve at each of its points, we can calculate the

curve. This is roughly the definition of integration is a small, but this is indefinite, that is,

that through this process, we can find the family of functions whose derivative is our given

function, now, we see that integration is defined and applications, which is the real reason

for this work

CLASS No 13



It makes me a little difference integral models.

What was easy?

I find it easy to resolve issues per ye comprehensive early models.


In this class I learned to develop and integrated problems with verification.


SECOND HALF OF RACE

CLASS No 14



DATE: Tuesday 08, Thursday, January 10, 2013.


CONTENTS:


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INTRODUCTION OF KNOWLEDGE:

Integral calculus: definition. Silva Laso, 1209, Smith, 475, Larson, 280

Differentials: definition.

Indefinite integral: definition

Mathematical models of support for immediate integration.

Project Exhibition


Define and calculate antiderivatives.

GENERAL DUTIES:

Definition and application of mathematical models indefinite integration.


SECOND HALF OF RACE

CLASS No 15





CONTENTS:

INTRODUCTION OF KNOWLEDGE:

Mathematical models of support for immediate integration. Smith, 475, Larson, 280

Project Exhibition


Define and calculate antiderivatives.

GENERAL DUTIES:


26/27

Definition and application of mathematical models indefinite integration.


SECOND HALF OF RACE

CLASS No 16





CONTENTS:

SUPPORTING RESEARCH WORK.

Type of Research.

Name of contribution.

IT tools.

Description.

Learning Objective.

Project duration.

Requirements.

Resources and materials.

activities and team teaching.

Evaluation Criteria.


Strengthen their knowledge potential.


27/27

Provide experiences.

Troubleshoot critics.

Link the team with the community and the family.

GENERAL DUTIES:

(ingles)calculo diferencial

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